Abstract
We consider the stepping stone model on the torus of side L in ℤ2 in the limit L→∞, and study the time it takes two lineages tracing backward in time to coalesce. Our work fills a gap between the finite range migration case of [Ann. Appl. Probab. 15 (2005) 671–699] and the long range case of [Genetics 172 (2006) 701–708], where the migration range is a positive fraction of L. We obtain limit theorems for the intermediate case, and verify a conjecture in [Probability Models for DNA Sequence Evolution (2008) Springer] that the model is homogeneously mixing if and only if the migration range is of larger order than (log L)1/2.
Citation
J. Theodore Cox. "Intermediate range migration in the two-dimensional stepping stone model." Ann. Appl. Probab. 20 (3) 785 - 805, June 2010. https://doi.org/10.1214/09-AAP639
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